CN113341372A - DOA estimation method based on decoherence unitary Root-MUSIC algorithm - Google Patents

DOA estimation method based on decoherence unitary Root-MUSIC algorithm Download PDF

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CN113341372A
CN113341372A CN202110607259.2A CN202110607259A CN113341372A CN 113341372 A CN113341372 A CN 113341372A CN 202110607259 A CN202110607259 A CN 202110607259A CN 113341372 A CN113341372 A CN 113341372A
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孙旭
吴鹏
黄广超
于文卓
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University of Electronic Science and Technology of China
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention discloses a DOA estimation method based on a decoherence unitary Root-MUSIC algorithm, which solves the problems that the DOA estimation method adopting a forward and backward space smoothing algorithm in the prior art is large in calculation amount, needs longer calculation time and is poor in timeliness. The invention comprises the following steps: dividing the equidistant uniform linear array into a plurality of overlapped sub-arrays; step 2: defining a new forward space smoothing algorithm, and estimating an improved forward space smoothing covariance matrix according to the new forward space smoothing algorithm; and step 3: calculating a new forward and backward space smoothing covariance matrix; and 4, step 4: unitary transformation is carried out on the forward and backward space smooth covariance matrix to obtain a real value symmetric matrix; and 5: performing characteristic decomposition on a real-valued symmetric matrix obtained after unitary transformation in a real number domain to obtain a noise subspace; step 6: and carrying out DOA estimation on the coherent signal by utilizing a Root-MUSIC algorithm. The invention reduces the calculated amount during DOA estimation, thereby realizing the accurate estimation of the signal DOA in a short time.

Description

DOA estimation method based on decoherence unitary Root-MUSIC algorithm
Technical Field
The invention belongs to the technical field of array signal processing, and particularly relates to a DOA estimation method based on a unitary Root-MUSIC algorithm of decoherence.
Background
Direction of Arrival (DOA) estimation has been an important research Direction in the field of array signal processing for the past decades, and has been widely used in radar, communication, investigation and other fields. The basic problem of DOA estimation is to determine the spatial location of multiple signals of interest (the direction angle of arrival of each signal at a reference array element of the array, referred to as the direction of arrival) that are simultaneously within a certain region of space. Beamforming is also essentially a direction-of-arrival estimation problem, except that they are non-parametric direction-of-arrival estimators. The resolution of these estimates depends on the array length. After the array length is determined, the resolution is also determined, called the rayleigh limit. The method of exceeding the rayleigh limit is called super resolution method. The earliest super-resolution DOA estimation methods were the well-known MUSIC method and ESPRIT method, which are the subspace methods of feature structure. The subspace method is based on a basic observation that if the number of sensors is larger than that of the signal sources, the signal components of the array data are positioned in a low-rank subspace, under a certain condition, the subspace uniquely determines the arrival direction of the signal, and the arrival direction can be accurately determined by using the singular value decomposition with stable values.
In an actual radar working environment, a radar radiates a transmitting signal into a space through a transmitting antenna, a target reflects the transmitting signal to form an echo signal, the surrounding environment of the target may have some obstacles such as tall buildings, trees and the like, the obstacles may reflect or scatter the echo signal reflected by the target, the echo signal may reach a receiving antenna through two or more than two propagation paths, the phenomenon is called multipath effect, the multipath effect may cause generation of a coherent signal, and a conventional DOA estimation algorithm such as a MUSIC algorithm, an ESPRIT algorithm, a Root-MUSIC algorithm and the like cannot effectively distinguish the coherent signal, so that a certain influence is generated on estimation of a target azimuth angle, and therefore, in order to obtain real azimuth information of the target, it is very important to eliminate the interference generated by the coherent signal.
For DOA estimation of coherent sources, a forward and backward spatial smoothing method and a matrix reconstruction method are generally adopted, wherein the forward and backward spatial smoothing is taken as a representative method. However, when the non-circular signal is used for DOA estimation, the original subspace structure is destroyed by directly applying the forward and backward spatial smoothing, so that a reliable DOA estimation result cannot be obtained. Therefore, how to fully utilize the characteristics of the non-circular signal to perform coherent source DOA estimation based on the single-base MIMO radar is an urgent technical problem to be solved.
When the forward and backward spatial smoothing algorithm is used for decoherence and then the MUSIC algorithm is used for DOA estimation, longer calculation time is needed and instantaneity is poor due to the fact that eigenvalue decomposition and spectral peak search are needed in a complex domain. And when the forward and backward space smoothing algorithm is used for estimating the coherent signal, the resolution ratio is lower
Common methods for decorrelation include a maximum likelihood method, a Toeplitz matrix reconstruction method, a spatial smoothing preprocessing method, and the like. The maximum likelihood method carries out coherent source signal processing through a probability density model, has a good decorrelation effect, but finally needs nonlinear multidimensional search to realize DOA estimation, and has huge calculation amount. The Yan Gao combined with the classical MUSIC algorithm proposed an Improved MUSIC (IMUSIC) algorithm for de-coherence processing. The greatest advantage of the IMUSIC algorithm is that there is no loss of array aperture, however, the algorithm can only perform effective de-coherence processing on two coherent source signals. The Toeplitz matrix reconstruction algorithm has the greatest advantage of no loss of array aperture, but the prior information of signals is not fully considered in the matrix reconstruction process, so that the estimation accuracy is relatively poor on occasions with different signal source powers. Spatial Smoothing Techniques (SST) were first proposed by Evans et al and subsequently improved by shann et al by a common and efficient solution intervention process. The decorrelation method is at the cost of sacrificing the effective aperture of the array, and in order to reduce the loss of the aperture of the array, pilai and the like propose a bidirectional spatial smoothing algorithm, namely a forward-backward spatial smoothing algorithm, on the basis of the previous research. When the forward and backward spatial smoothing algorithm is used for decoherence and then the MUSIC algorithm is used for DOA estimation, longer calculation time is needed and instantaneity is poor due to the fact that eigenvalue decomposition and spectral peak search are needed in a complex domain.
Disclosure of Invention
Aiming at the problems that in the prior art, a DOA estimation method adopting a forward and backward space smoothing algorithm needs longer calculation time and is poor in timeliness, the invention provides a DOA estimation method based on a unitary Root-MUSIC algorithm with decoherence, and the DOA estimation method is aimed at: the calculation amount is reduced, and the accuracy and the timeliness of DOA estimation are improved.
The technical scheme adopted by the invention is as follows:
a DOA estimation method based on a decoherence unitary Root-MUSIC algorithm comprises the following steps:
step 1: dividing the equidistant uniform linear array into a plurality of overlapped sub-arrays;
step 2: defining a new forward spatial smoothing algorithm, and estimating an improved forward spatial smoothing covariance matrix according to the new forward spatial smoothing algorithm, wherein the new forward spatial smoothing algorithm is as follows:
Figure RE-GDA0003137635440000021
where M is the number of mutually overlapping sub-arrays,
Figure RE-GDA0003137635440000022
covariance of output data for the new forward spatial smoothing algorithm, R is covariance of output data before no subarray division operation, R isijFor a matrix of dimensions k x k with the elements of i rows and j columns as the upper left corner elements, Rji、Rii、RjjThe same process is carried out;
and step 3: calculating a new forward and backward space smoothing covariance matrix, wherein the calculation formula is as follows:
Figure RE-GDA0003137635440000023
in the formula
Figure RE-GDA0003137635440000024
Improved forward and backward spatial smoothing algorithmA covariance matrix; j is a switching matrix with a minor diagonal element of 1 and the other elements of 0; represents a conjugate matrix;
and 4, step 4: unitary transformation is carried out on the forward and backward space smooth covariance matrix to obtain a real value symmetric matrix;
and 5: performing characteristic decomposition on a real-valued symmetric matrix obtained after unitary transformation in a real number domain to obtain a noise subspace;
step 6: and carrying out DOA estimation on the coherent signal by utilizing a Root-MUSIC algorithm.
Preferably, the specific steps of the unitary transformation in step 4 are as follows:
order to
Figure RE-GDA0003137635440000031
Matrix R0For a centro-Hermitian matrix, the matrix R is modified according to the properties of the centro-Hermitian matrix0Converting into a real-valued symmetric matrix, namely:
Rreal＝UHR0U
in the formula, RrealRepresenting the transformed real-valued symmetric matrix, U representing the unitary matrix, UHRepresenting the conjugate transpose of the unitary matrix.
Preferably, when R is0For odd and even order matrices, the corresponding unitary matrix U is represented as:
Figure RE-GDA0003137635440000032
Figure RE-GDA0003137635440000033
in the formula, JnIs an inverse identity matrix of dimension n x n, InAn identity matrix representing dimensions n x n, j being
Figure RE-GDA0003137635440000034
Due to the adoption of the technical scheme, the invention has the beneficial effects that:
to the covariance matrix R obtained after processing0Only the real-value symmetric matrix R needs to be considered when the eigenvalue decomposition is carried outrealThe eigenvalue decomposition is carried out, the eigenvalue decomposition of the real-valued matrix is only carried out in a real number domain, the operation amount is greatly reduced, and then the Root-MUSIC algorithm is used for estimating the arrival angle of the signal, so that the operation amount and the time loss caused by spectral peak search are reduced.
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The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of a decoherence unitary Root-MUSIC algorithm;
FIG. 2 is a Root distribution graph of the decoherence unitary Root-MUSIC algorithm at signal directions of-10 °, 0 °, and 10 °;
FIG. 3 is a comparison graph of DOA estimation results of the decorrelation algorithm at-10 °, 0 ° and 10 ° signal directions;
FIG. 4 is a Root distribution graph of the decoherence unitary Root-MUSIC algorithm with signal directions of-6 °, 0 °, and 6 °;
FIG. 5 is a comparison graph of DOA estimation results by the decorrelation algorithm for signal directions of-6 °, 0 °, and 6 °;
FIG. 6 is a root mean square error of a decorrelating DOA estimation algorithm at different signal-to-noise ratios;
fig. 7 is the root mean square error of the decorrelating DOA estimation algorithm at different snapshot counts.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
In the description of the embodiments of the present application, it should be noted that the terms "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings or orientations or positional relationships that the products of the present invention are usually placed in when used, and are only used for convenience of description and simplicity of description, but do not indicate or imply that the devices or elements that are referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present application. Furthermore, the terms "first," "second," "third," and the like are used solely to distinguish one from another and are not to be construed as indicating or implying relative importance.
Example 1
A DOA estimation method based on a decoherence unitary Root-MUSIC algorithm comprises the following steps:
step 1: dividing the equidistant uniform linear array into a plurality of overlapped sub-arrays;
step 2: defining a new forward spatial smoothing covariance matrix:
Figure RE-GDA0003137635440000041
where M is the number of mutually overlapping sub-arrays,
Figure RE-GDA0003137635440000042
covariance of output data for the new forward spatial smoothing algorithm, R is covariance of output data before no subarray division operation, R isijFor a matrix of dimensions k x k with the elements of i rows and j columns as the upper left corner elements, Rji、Rii、RjjThe same process is carried out;
and step 3: calculating a new forward and backward space smoothing covariance matrix, wherein the calculation formula is as follows:
Figure RE-GDA0003137635440000043
in the formula
Figure RE-GDA0003137635440000044
A covariance matrix corresponding to the improved forward and backward spatial smoothing algorithm; j is a switching matrix with a minor diagonal element of 1 and the other elements of 0; represents a conjugate matrix;
and 4, step 4: order to
Figure RE-GDA0003137635440000045
Then matrix R0Is a centro-Hermitian matrix, and the matrix R is known from the properties of the centro-Hermitian matrix0Can be converted into a real-valued symmetric matrix, namely:
Rreal＝UHR0U
in the formula, RrealRepresenting the transformed real-valued symmetric matrix, U representing the unitary matrix, UHRepresenting the conjugate transpose of the unitary matrix.
When R is0For odd and even order matrices, the corresponding unitary matrix U is represented as:
Figure RE-GDA0003137635440000051
Figure RE-GDA0003137635440000052
in the formula, JnIs an inverse identity matrix of dimension n x n, InAn identity matrix representing dimensions n x n, j being
Figure RE-GDA0003137635440000053
And 5: performing characteristic decomposition on a real-valued symmetric matrix obtained after unitary transformation in a real number domain to obtain a noise subspace;
step 6: and carrying out DOA estimation on the coherent signal by utilizing a Root-MUSIC algorithm.
By adopting the method, the covariance matrix R obtained after the processing0Only the real-value symmetric matrix R needs to be considered when the eigenvalue decomposition is carried outrealThe eigenvalue decomposition is carried out, the eigenvalue decomposition of the real-valued matrix is only carried out in a real number domain, the operation amount is greatly reduced, and then the Root-MUSIC algorithm is used for estimating the arrival angle of the signal, so that the operation amount and the time loss caused by spectral peak search are reduced.
In order to verify the decoherence capability of the decoherence unitary Root-MUSIC algorithm provided by the scheme, the following computer simulation experiment is carried out in the patent. The present invention is described in detail below with reference to fig. 1 to 7.
Experiment 1: the receiving array is assumed to be a uniform linear array with 8 array elements, the array element spacing is lambda/2, three coherent signals exist in the space and are respectively positioned at the azimuth angles (-10 degrees, 0 degrees and 10 degrees) of the radar, the signal-to-noise ratio is 10dB, and the fast beat number is 250. And performing DOA estimation on the signal by utilizing a MUSIC algorithm, a forward and backward space smoothing MUSIC algorithm and a decoherence unitary Root-MUSIC algorithm, wherein the spatial spectrum search range is-60 degrees, and the search step is 0.1 degree. The array element number of the sub-arrays in the forward and backward space smoothing MUSIC algorithm and the decoherence unitary Root-MUSIC algorithm is 6, and the total number of the forward sub-arrays and the total number of the backward sub-arrays are both 3. Fig. 2 is a Root distribution diagram calculated by the decoherence unitary Root-MUSIC algorithm, and DOA estimation results simulated by the three algorithms are shown in fig. 3.
The Root results obtained by the unitary decorrelating Root-MUSIC algorithm under the above experimental conditions are shown in fig. 2, and DOA estimated values of-10.0049 °, 0.1231 ° and 9.9602 ° are obtained by using the following equations according to the phases corresponding to the three roots. The DOA estimation results of the three algorithms are compared in fig. 3, and when only coherent signals exist in the space, the forward and backward spatial smoothing MUSIC algorithm and the decorrelation unitary Root-MUSIC algorithm can accurately estimate the arrival angle of the signals, and the MUSIC algorithm completely fails under the condition.
Table 1 shows the statistical results of the time overhead of signal DOA estimation performed by the decorrelating unitary Root-MUSIC algorithm and the forward-backward spatial smoothing MUSIC algorithm, which varies with the estimation accuracy.
TABLE 1 time consuming comparison of two decorrelating DOA estimation algorithms at varying estimation accuracy
Figure RE-GDA0003137635440000054
Figure RE-GDA0003137635440000061
As can be seen from the table, the estimation accuracy can affect the computation time of the forward and backward spatial smoothing MUSIC algorithm, and when the estimation accuracy is reduced, the algorithm time is increased; the estimation time of the decorrelation unitary Root-MUSIC algorithm is not influenced by the estimation precision. Compared with a forward and backward space smoothing MUSIC algorithm, the decoherence unitary Root-MUSIC algorithm provided by the invention can obviously reduce the calculation time when carrying out DOA estimation on the signal. The coherent unitary Root-MUSIC algorithm can complete the estimation of noise subspace and signal subspace in a real number domain by performing unitary transformation on a covariance matrix, and thoroughly avoids peak search due to the adoption of the Root-MUSIC algorithm when DOA estimation is performed, so that the coherent unitary Root-MUSIC algorithm can greatly reduce the calculation amount when DOA estimation is performed, and accurate estimation of signal DOA can be completed in a short time.
Experiment 2: experiment 2 is identical to experiment 1 in experimental conditions, but the incident angle of the signal is changed, and the azimuth angles of the source relative to the array are (-6 degrees, 0 degrees and 6 degrees) respectively and are coherent signals. In this case, the DOA estimation is performed on the signal using the MUSIC algorithm, the forward-backward spatial smoothing MUSIC algorithm, and the decorrelating unitary Root-MUSIC algorithm. Fig. 4 is a Root distribution graph calculated by the decoherence unitary Root-MUSIC algorithm, and DOA estimation results simulated by the three algorithms are shown in fig. 5.
The Root results obtained by the unitary decorrelating Root-MUSIC algorithm under the above experimental conditions are shown in fig. 4, and according to the phases corresponding to the three roots, DOA estimated values obtained by using the formula are 4.7881 °, -4.7829 ° and 0.4136 °, respectively, and the unitary decorrelating Root-MUSIC algorithm can still effectively distinguish the three coherent signals. In fig. 5, the DOA estimation results of the three algorithms are compared, and it can be seen from the curves of the spatial spectrum that the MUSIC algorithm still cannot resolve the coherent signals, and the forward and backward spatial smoothing algorithm only has two peak poles in this case, which means that the forward and backward spatial smoothing algorithm has lost the ability to resolve the three coherent signals.
Experiment 3: assuming that the receiving array is a uniform linear array with 8 array elements, the array element spacing is lambda/2, the fast beat number is 250, the signal-to-noise ratio is taken from-15 dB to 15dB at intervals of 1dB, 1000 independent experiments are carried out under the condition that the signal-to-noise ratio of each value is fixed, and in each experiment, two coherent signals exist in the space and are respectively positioned at the (0 DEG and 10 DEG) azimuth angles of the array. Wherein, the search range of the spatial spectrum is-60 degrees to 60 degrees, and the search step is 0.1 degree. The receiving array is subjected to DOA estimation by respectively utilizing a forward and backward space smoothing MUSIC algorithm and a decoherence unitary Root-MUSIC algorithm, and the Root Mean Square Error (RMSE) of the two decoherence super-resolution DOA estimation algorithms under the conditions of different signal-to-noise ratios is shown in figure 6.
As can be seen from fig. 6, as the SNR increases, the RMSE of both decorrelation algorithms gradually decreases, i.e., the DOA estimation accuracy becomes better and better, the two are very close to each other, and the error is not very large. However, the estimation error of the decoherence unitary Root-MUSIC algorithm proposed herein is almost always lower than that of the forward-backward spatial smoothing algorithm.
Experiment 4: the receiving array is assumed to be a uniform linear array with 8 array elements, the spacing between the array elements is lambda/2, the signal-to-noise ratio is 10dB, the fast-beat number is taken from 100 to 500 at an interval of 20, 1000 independent experiments are carried out under the condition that the fast-beat number of each value is fixed, and in each experiment, two coherent signals exist in the space and are respectively positioned at the (0 degree and 10 degree) azimuth angles of the array. Wherein, the search range of the spatial spectrum is-60 degrees to 60 degrees, and the search step is 0.1 degree. The receiving array is subjected to DOA estimation by respectively utilizing a forward and backward space smoothing MUSIC algorithm and a decoherence unitary Root-MUSIC algorithm, and the Root Mean Square Error (RMSE) of the two decoherence super-resolution DOA estimation algorithms under the conditions of different snapshot numbers is shown in figure 7.
The above-mentioned embodiments only express the specific embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for those skilled in the art, without departing from the technical idea of the present application, several changes and modifications can be made, which are all within the protection scope of the present application.

Claims (3)

1. A DOA estimation method based on a decoherence unitary Root-MUSIC algorithm is characterized by comprising the following steps:
step 1: dividing the equidistant uniform linear array into a plurality of overlapped sub-arrays;
step 2: defining a new forward spatial smoothing algorithm, and estimating an improved forward spatial smoothing covariance matrix according to the new forward spatial smoothing algorithm, wherein the new forward spatial smoothing algorithm is as follows:
Figure FDA0003092008430000011
where M is the number of mutually overlapping sub-arrays,
Figure FDA0003092008430000012
covariance of output data for the new forward spatial smoothing algorithm, R is covariance of output data before no subarray division operation, R isijFor a matrix of dimensions k x k with the elements of i rows and j columns as the upper left corner elements, Rji、Rii、RjjThe same process is carried out;
and step 3: calculating a new forward and backward space smoothing covariance matrix, wherein the calculation formula is as follows:
Figure FDA0003092008430000013
in the formula
Figure FDA0003092008430000014
A covariance matrix corresponding to the improved forward and backward spatial smoothing algorithm; j is a switching matrix with a minor diagonal element of 1 and the other elements of 0; represents a conjugate matrix;
and 4, step 4: unitary transformation is carried out on the forward and backward space smooth covariance matrix to obtain a real value symmetric matrix;
and 5: performing characteristic decomposition on a real-valued symmetric matrix obtained after unitary transformation in a real number domain to obtain a noise subspace;
step 6: and carrying out DOA estimation on the coherent signal by utilizing a Root-MUSIC algorithm.
2. The DOA estimation method based on the decoherence unitary Root-MUSIC algorithm of claim 1, wherein the unitary transformation in step 4 comprises the following specific steps:
order to
Figure FDA0003092008430000015
Matrix R0For a centro-Hermitian matrix, the matrix R is modified according to the properties of the centro-Hermitian matrix0Converting into a real-valued symmetric matrix, namely:
Rreal＝UHR0U
in the formula, RrealRepresenting the transformed real-valued symmetric matrix, U representing the unitary matrix, UHRepresenting the conjugate transpose of the unitary matrix.
3. The DOA estimation method based on the unitary Root-MUSIC algorithm of decoherence of claim 2, wherein R is the time when R is0For odd and even order matrices, the corresponding unitary matrix U is represented as:
Figure FDA0003092008430000021
Figure FDA0003092008430000022
in the formula, JnIs an inverse identity matrix of dimension n x n, InAn identity matrix representing dimensions n x n, j being
Figure FDA0003092008430000023
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Application publication date: 20210903